nLab Szpiro's conjecture

A statement about elliptic curves.

Relation to other statements

In its general form, equivalent to the abc conjecture.

If Mochizuki's corollary 3.12 is true, then Szpiro’s conjecture is also true.

References

• Wikipedia, Szpiro’s conjecture

The relation to the abc conjecture is discussed in

• Matt Baker (notes taken by William Stein), Elliptic curves, the ABC conjecture, and points of small canonical height (pdf)

The relation to Mochizuki's corollary 3.12 is discussed in

• Taylor Dupuy, Anton Hilado, Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki’s Corollary 3.12 [arxiv:2004.13108]